Exploring Promising Concepts in Cosmology and Geometry

Which holds the most promise?

by Bruce E. Camber with assists from five AI platforms

Abstract.
Six concepts, an alternative start of our universe, build on each other.
1. Singularity-free origin: Proposes a universe starting at the Planck scale with infinitesimal spheres that are initially organized geometrically. Links for more (below).
2. Base-2 scaling: The universe’s expansion is cataloged through a series of 202 base-2 notations, with the length and time scale doubling at each step. For more: https://81018.com/chart/
3. Role of geometry and symmetry: Emphasizes the role of geometry and continuity-symmetry-harmony of pi(𝜋), then extends it to the other mathematical properties of other irrational numbers in shaping the universe and driving its expansion. https://81018.com/planck-polyhedral-core/
4. The role of 18.5 tredecillion PlanckSpheres per second generated at one unit per Planck Time, this rate (18.5 × 10⁴³ spheres/second) aligns with the Hubble constant (~71 km/s/Mpc), implying dense, flawless packing in early notations.
Homepage: https://81018.com/hubble-derivation/
Grok: https://81018.com/hubble-constant/
ChatGPT: https://81018.com/toy-model-derivation-of-the-hubble-constant/
5. The role of geometric gaps (e.g., 7.358+° naturally in clusters as five tetrahedrons or five octahedrons) initiate quantum indeterminacy. A redefinition of infinity as continuity-symmetry-harmony: https://81018.com/biased/#Aristotle and https://81018.com/csh/
6. Role of ethics and values as continuity-symmetry-harmony: A brief exploration in value and even ethics. It is detailed: http://81018.com/ethics/ and https://81018.com/qualitative-expansion/

Introduction

Elements of these six concepts have been discussed since 2011. It seemed this work was necessarily always going to be “in process.” Some of these key points have been part of our discussions since the 1970s. Yet, today’s AI tools seem to be changing that forever. There is consensus building among AI platforms and that consensus will have a special logic. Even so, there’ll be scholars slow to join them, but they will.

The focus will first be with the biggest riddles and unsolved mysteries, questions that have been holding back the progress of science. Such a key question is: “How did the universe start?”

None of us want to be absurd to ourselves. We grew up with the big bang theory. Although there have always been dissenters and even those with alternative theories. None have been complete or compelling enough. Even today, Google AI reminds those of us whose ideas are not part of the main stream. Thanks, Google.

Discussion

October 2025: We asked an AI, DeepSeek, “Which concept holds the most promise to answer these most probing questions in cosmology and physics and why?” DeepSeek’s answer blew us away. Originated with entrepreneurs in China, this low-cost, high-performing AI platform is much like those developed in the USA. It seemed to affirm the direction of our work.

Also in October 2025, Anthropic responded to very similar questions. The results were most-positive with great suggestions. We are now asking more and more AI platforms questions about these six concepts and this is our first report of the results.

This is the first time we have received immediate feedback and encouragement since starting in December 2011 and even going back to our first ideas 1972. At long last, we could take ourselves a little more seriously! We need to do that because the challenges ahead are formidable.

The Finite-Infinite Dilemma: The First Spheres are in Notation-0. Our thinking today is that more happens within the infinite than prior discussed in the literature (at least, in the works that we’ve studied). We had already imparted the qualitative and “continuity, symmetry, and harmony” to the infinite. We had concluded, “Emergence starts with the qualitative infinite and becomes the quantitative finite.” The never-ending, never-repeating numbers defined the infinitesimal spheres. Actual numbers were by the Planck base units (or equivalents), and it was still an infinite network with an inherent geometry. Our Planck Polyhedral Core emerged as tetrahedrons and octahedrons. The universe’s initial entity, encapsulating space-time via equations involving the speed of light (c), gravitational constant (G), reduced Planck constant (ℏ), and pi (π), was a tetrahedral-octahedral complex. It looks like automorphic forms in one direction and strings in the other.

These units delineate the inaugural instant of space-time, matter-energy, and fundamental forces like gravity and electromagnetism.

Since 2016, our analyses have centered on pi (π) and spheres as foundational. By 2019, pi’s role expanded; in 2025, a polyhedral geometry emerged, linking finite and infinite realms via pi and three other irrationals (e, √2, φ). This sphere inhabits a hypostatic domain of forms, akin to automorphic structures, on the finite-infinite bridge and on the way to defining the first moment of spacetime.

First Hypostatic Actions: Call them hypostatic spheres that spin, stack, and pack, centers instantly connecting, shaping hypostatic tetrahedrons then octahedrons, the geometric building blocks of the first temporal moment. These were above and beyond our earlier conclusions: https://81018.com/spheres-symphony/ https://81018.com/sphere/ https://81018.com/spheres/

Hypostatic Spinning, Stacking, Packing, Centering, Triangulating on the finite-infinte bridge

Everyday spheres (e.g., baseballs) are familiar, but celestial rotations (planets, stars) hint at deeper dynamics. Imagine Planck-scale spheres spinning at extraordinary rates—lab records reach 300 billion rpm, while neutron stars hit 716 revolutions/second. In this model, octahedral emissions create spinning spheres that stack, pack, discover abutting centers, then become archetypal tetrahedrons and octahedrons. Early notations (1-64) encompass spin states, forms, strings, geometries, substances, qualities, relations, and systems, leading to hypothetical particles by notation 50-60.

These domains embody “perfection,” with no room for imperfections until notations 64-67, where measurable fluctuations arise (charted in our 2013 models).

Conclusions

Complexities of the First Moment: Octahedral structures reveal four hexagonal plates, hypothesized as the finite-infinite interface.

18.5 Tredecillion Spheres per Second: Generated at one per Planck time, this rate (18.5 × 10⁴³ spheres/second) aligns with the Hubble constant (~71 km/s/Mpc), implying dense, flawless packing in early notations.

202 Notations Make the Universe: The cosmos is divided into 202 exponential doublings (notations), from Planck scales to the present, first charted in a 2011 high school geometry class.

Pi (π) Shapes Our Universe: Pi embodies continuity, symmetry, and harmony from infinity, with other irrationals revealing additional facets.

Quantum Fluctuations: Natural geometric gaps (e.g., 7.358+° naturally in clustered as five tetrahedrons or five octahedrons) initiate quantum indeterminacy.